Maths Formulae
Notation \lfloor x \rfloor - Round down x \lceil x \rceil - Round up x \sum_{n=1}^{N} n = 1 + 2 + 3 + 4 + ... + N - Sigma notation for summing terms from 1 to N (example function is just n) |x| = x (x > 0) The modulus / absolute value function ( |0| = 0 ) |x| = -x (x < 0) General Summation Arithmetic series (of the form a_n = a_1 + (n-1)d ) From 1 to N: S_N = \sum_{n=1}^{N}a_n = \frac{N}{2}(2a_1 + (N-1)d) Geometric series (of the form a_n = {a_1}{r^{(n-1)}} ) From 1 to N: S_N = \sum_{n=1}^{N}a_n = \frac (\frac{5n-80}{25})^{1.3}\right ) These formulae don't take into account Black Eggs gained from Rebirth Power however. The Rebirth Power BE equations are: BlackEggs = (10\times (Earth Egg Level)^2+1)\times \left( 20\times (1+Multiplier)^{\frac{level}{5}-20} + {\left (\frac{level-80}{25} \right )^{1.3}} \right ) Where: Multiplier = \frac{1}{100}(25-23\times {e^{-0.0003\times GoldenEggs}}) Golden Eggs (GE) To obtain the total number of Golden Eggs you have from the total Black Eggs you've earned: GE = 5\log_{10} (BE) If you already have Golden Eggs, you need to know how many Black Eggs you've earned in total (if you speak to the Phoenix it will tell you) to work out how many more black eggs you need for another Golden Egg. NewGE = 5\log_{10} (\frac{NewBE}{PreviousBE}) Rebirth Power (RP) Rebirth power as a percentage: RP = 25 - 23(e^{-0.0003(GE)}) In this case GE is the total number of GE you need in order to give a certain Rebirth Power (RP) GE = \frac{\ln (\frac{23}{25-RP})}{0.0003} Easter Eggs There are 3 different cost scaling types for Easter Eggs: Exponential Cost Scaling These Easter Eggs have an upgrade cost of 2^{(n+1)} , where n is the current level. This can reduced by upgrading Water Egg but the scaling will remain exponential in nature. * Cactus * Garbage * Hourglass * Idol * King Cobra * Ninja * Present * Radio * Radioactive * Scientist * Super * Treasure * Unstable The relevant formulae for these Easter Eggs are then: LevelUpCost = 2^{(CurrentLevel + 1)} CumulativeCost = 2^{(CurrentLevel + 1)} - 3 For a given number of black eggs, the number of levels that can be bought is: Levels = \lfloor {\log_2{(BE + 1)} - 1}\rfloor Linear Cost Scaling These Easter Eggs have a an upgrade cost that is directly proportional to the level of the Easter Egg. * Demeaning * Dragon * Eggplant * Faberge * Newton * Wonderland Relevant formulae: LevelUpCost = (CurrentLevel + 1) CumulativeCost = \frac{1}{2}(CurrentLevel)(CurrentLevel + 1) For a given number of black eggs, the number of levels that can be bought is: Levels = \lfloor {\sqrt{(2BE + 0.25)} - 0.5}\rfloor Constant Cost Phoenix Eggs All of the Phoenix Eggs have upgrade costs that scale linearly with level apart from Fire Egg. Linear Cost Scaling * Acid * Earth * Electricity * Magnetism * Sound * Water * Wind Relevant formulae: LevelUpCost = (CurrentLevel + 1) CumulativeCost = \frac{1}{2}(CurrentLevel)(CurrentLevel + 1) For a given number of Golden Eggs, the number of levels that can be bought is: Levels = \lfloor {\sqrt{(2GE + 0.25)} - 0.5}\rfloor Constant Cost * Fire Chickens Category:Info Category:Guides and Tips Category:Game Mechanics Category:Gameplay Mechanics Category:Currency Category:Exponential Cost Scaling Easter Eggs Category:Linear Cost Scaling Easter Eggs Category:Constant Cost Scaling Easter Eggs Category:Maths Formulae